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Find the linear approximation of the function $g(x)=\sqrt[3]{1+x}$ at $a=0$ and use it to approximate the numbers $\sqrt[3]{0.95}$ and $\sqrt[3]{1.1}$ . Illustrate by graphing $g$ and the tangent line.

$L(x)=1+\frac{1}{3}(x-a)=1+\frac{1}{3} x$$L(0.05)=1-\frac{1}{3} 0.05=0.9833333$$L(-0.1)=1+\frac{1}{3} 0.1=1.033333$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Oregon State University

Harvey Mudd College

University of Nottingham

Lectures

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In mathematics, precalculu…

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In mathematics, a function…

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Find the linear approximat…

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(a) Find the local linear …

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Verify the given linear ap…

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Using a Tangent Line Appro…

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Find a function $f$ such t…

Compute the linear approxi…

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Linear approximation a. Fi…

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Suppose $f$ is differentia…

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Find the lincar approximat…

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Linear approximation Find …

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in this problem. We're given a function G anywhere. Esther. The year in the right spot. Joanna used at airports. Mate, you know. So let's start with writing function. G s one plus extra probable heard. And let's find a day with Tochigi Perm affects would be 1/3 well plus eggs. Negative two firms. So now, unless you let the functions of every threat given point Sarge easier. Zero text Joe would be one and g primal zero b. We'll burn so that the musicians function, uh, is G zero plus g prime zero explain. It's given point. So zero on from this. This would be one plus. We'll third. Oh, yes. So the first what we're given is going by. So this is a cook, too. One was negative. Orange. You're high. So if you plug nectar is your part in X, we find this to be one plus 1/3 of negatives. You're five. Then this is 50.983 2nd 1 is won'th boy form, and that is ICO to one plus one. So we're gonna put point fun. One, uh, warm was 1/3 0.1 and we find it to be one point zero

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